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  • Need solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 11

Need solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 11

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Answer: Parallelogram

Hint: Find ABCD

Given: If  \vec{a}, \vec{b}, \vec{c} \; \&\; \vec{d}  are position vectors of points A,B,C and D  such that no three of them are collinear  \vec{a}+\vec{c}=\vec{b}+\vec{d}  then ABCD is

Solution: Given \vec{a}+\vec{c}=\vec{b}+\vec{d}

                        \begin{aligned} &\vec{c}-\vec{d}=\vec{b}-\vec{a} \\ \\ &\overrightarrow{A B}=\overrightarrow{D C} \text { and } \vec{a}+\vec{c}=\vec{b}+\vec{d} \\ \\ &\vec{c}-\vec{d}=\vec{b}-\vec{a} \\ \\ &\overrightarrow{A D}=\overrightarrow{B C} \end{aligned}

               Since \vec{a}+\vec{c}=\vec{b}+\vec{d}

            \frac{1}{2}(\vec{a}+\vec{c})=\frac{1}{2}(\vec{b}+\vec{d})

            So position vector midpoint of BD =  position vector of midpoint of AC

            Hence bisect each other

            The given point ABCD is parallelogram.

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